Magic Cube

///////////////////////////////////////////////////////////////////////////////////////////////////

// Copyright 2020 Leszek Koltunski                                                               //

//                                                                                               //

// This file is part of Magic Cube.                                                              //

//                                                                                               //

// Magic Cube is free software: you can redistribute it and/or modify                            //

// it under the terms of the GNU General Public License as published by                          //

// the Free Software Foundation, either version 2 of the License, or                             //

// (at your option) any later version.                                                           //

//                                                                                               //

// Magic Cube is distributed in the hope that it will be useful,                                 //

// but WITHOUT ANY WARRANTY; without even the implied warranty of                                //

// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                                 //

// GNU General Public License for more details.                                                  //

//                                                                                               //

// You should have received a copy of the GNU General Public License                             //

// along with Magic Cube.  If not, see <http://www.gnu.org/licenses/>.                           //

///////////////////////////////////////////////////////////////////////////////////////////////////

package org.distorted.objects;

import android.content.res.Resources;

import android.graphics.Canvas;

import android.graphics.Paint;

import org.distorted.library.effect.MatrixEffectQuaternion;

import org.distorted.library.main.DistortedEffects;

import org.distorted.library.main.DistortedTexture;

import org.distorted.library.mesh.MeshBase;

import org.distorted.library.mesh.MeshSquare;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

import org.distorted.main.R;

import org.distorted.main.RubikSurfaceView;

import static org.distorted.objects.FactoryCubit.COS18;

import static org.distorted.objects.FactoryCubit.COS54;

import static org.distorted.objects.FactoryCubit.SIN18;

import static org.distorted.objects.FactoryCubit.SIN54;

///////////////////////////////////////////////////////////////////////////////////////////////////

public class TwistyKilominx extends TwistyMinx

{

  private static MeshBase[] mCenterMeshes, mCornerMeshes;

  private static MeshBase[][] mEdgeMeshes;

  private static final int[] mCenterFaceMap = new int[]

      {

        0,0,0,0,1,

        1,0,1,1,0,

        2,0,1,1,0,

        2,2,1,0,2,

        2,1,0,0,1,

        1,2,0,1,0,

        0,1,0,1,1,

        0,1,0,2,0,

        2,1,2,2,2,

        1,0,2,1,2,

        2,1,0,1,2,

        2,2,2,2,2

      };

  private static final int mNumCornerEdgeVariants;

  static

    {

    int[] sizes = ObjectList.KILO.getSizes();

    int variants = sizes.length;

    mNumCornerEdgeVariants = sizes[0]==3 ? variants-1 : variants;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  TwistyKilominx(int size, Static4D quat, DistortedTexture texture, MeshSquare mesh,

                 DistortedEffects effects, int[][] moves, Resources res, int scrWidth)

    {

    super(size, size, quat, texture, mesh, effects, moves, ObjectList.KILO, res, scrWidth);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private int numCubitsPerCorner(int numLayers)

    {

    return 3*((numLayers-3)/2)*((numLayers-5)/2) + (numLayers<5 ? 0:1);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private int numCubitsPerEdge(int numLayers)

    {

    return numLayers<5 ? 0 : 2*(numLayers-4);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getNumStickerTypes(int numLayers)

    {

    return numLayers<5 ? 1 : numLayers/2 + 1;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  float getScreenRatio()

    {

    return 1.00f;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  float[] getCuts(int numLayers)

    {

    float[] cuts = new float[numLayers-1];

    float D = numLayers*MovementMinx.DIST3D;

    float E = 2*C1;           // 2*cos(36 deg)

    float X = 2*D*E/(1+2*E);  // height of the 'upper' part of a dodecahedron, i.e. put it on a table,

                              // its height is then D*2*DIST3D, it has one 'lower' part of height X, one

                              // 'middle' part of height Y and one upper part of height X again.

                              // It's edge length = numLayers/3.0f.

    int num = (numLayers-1)/2;

    float G = X*0.5f/num;     // height of one Layer

    for(int i=0; i<num; i++)

      {

      cuts[        i] = -D + (i+0.5f)*G;

      cuts[2*num-1-i] = -cuts[i];

      }

    return cuts;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// Fill out mCurrCorner{X,Y,Z} by applying appropriate Quat to mBasicCorner{X,Y,Z}

// Appropriate one: QUATS[QUAT_INDICES[corner]].

  private void computeBasicCornerVectors(int corner)

    {

    Static4D quat = QUATS[QUAT_CORNER_INDICES[corner]];

    mCurrCornerV[0] = RubikSurfaceView.rotateVectorByQuat(mBasicCornerV[0],quat);

    mCurrCornerV[1] = RubikSurfaceView.rotateVectorByQuat(mBasicCornerV[1],quat);

    mCurrCornerV[2] = RubikSurfaceView.rotateVectorByQuat(mBasicCornerV[2],quat);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private float[] computeCorner(int numCubitsPerCorner, int numLayers, int corner, int part)

    {

    float D = numLayers/3.0f;

    float[] corn = CORNERS[corner];

    if( part==0 )

      {

      return new float[] { corn[0]*D, corn[1]*D, corn[2]*D };

      }

    else

      {

      float E = D/(0.5f*(numLayers-1));   // ?? maybe 0.5*

      int N = (numCubitsPerCorner-1)/3;

      int block = (part-1) % N;

      int index = (part-1) / N;

      Static4D pri = mCurrCornerV[index];

      Static4D sec = mCurrCornerV[(index+2)%3];

      int layers= (numLayers-5)/2;

      int multP = (block % layers) + 1;

      int multS = (block / layers);

      return new float[] {

                          corn[0]*D + (pri.get0()*multP + sec.get0()*multS)*E,

                          corn[1]*D + (pri.get1()*multP + sec.get1()*multS)*E,

                          corn[2]*D + (pri.get2()*multP + sec.get2()*multS)*E

                         };

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private float[] computeCenter(int numLayers, int center, int part)

    {

    int corner = mCenterMap[center][part];

    float[] cent = mCenterCoords[center];

    float[] corn = CORNERS[corner];

    float D = numLayers/3.0f;

    float F = 1.0f - (2.0f*numLayers-6.0f)/(numLayers-1)*COS54*COS54;

    return new float[]

      {

        D * ( cent[0] + (corn[0]-cent[0])*F),

        D * ( cent[1] + (corn[1]-cent[1])*F),

        D * ( cent[2] + (corn[2]-cent[2])*F)

      };

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private int computeEdgeType(int cubit, int numCubitsPerCorner, int numCubitsPerEdge)

    {

    int part = (cubit - NUM_CORNERS*numCubitsPerCorner) % numCubitsPerEdge;

    return part - 2*(part/4);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private float[] computeEdge(int numLayers, int edge, int part)

    {

    float D = numLayers/3.0f;

    float[] c1 = CORNERS[ mEdgeMap[edge][0] ];

    float[] c2 = CORNERS[ mEdgeMap[edge][1] ];

    int leftRight = 2*(part%2) -1;

    part /= 2;

    if( part==0 )

      {

      float T = 0.5f + leftRight/(numLayers-1.0f);

      float x = D * (T*c1[0]+(1.0f-T)*c2[0]);

      float y = D * (T*c1[1]+(1.0f-T)*c2[1]);

      float z = D * (T*c1[2]+(1.0f-T)*c2[2]);

      return new float[] { x, y, z };

      }

    else

      {

      int mult = (part+1)/2;

      int dir  = (part+1)%2;

      float[] center = mCenterCoords[ mEdgeMap[edge][dir+2] ];

      float x = 0.5f * D * (c1[0]+c2[0]);

      float y = 0.5f * D * (c1[1]+c2[1]);

      float z = 0.5f * D * (c1[2]+c2[2]);

      float vX = D*center[0] - x;

      float vY = D*center[1] - y;

      float vZ = D*center[2] - z;

      float T = 0.5f + leftRight*(mult*SIN18 + 1.0f)/(numLayers-1);

      x = D * (T*c1[0]+(1.0f-T)*c2[0]);

      y = D * (T*c1[1]+(1.0f-T)*c2[1]);

      z = D * (T*c1[2]+(1.0f-T)*c2[2]);

      float H = mult*D*COS18/(numLayers-1);

      H /= (float)Math.sqrt(vX*vX+vY*vY+vZ*vZ);

      return new float[] { x + H*vX, y + H*vY, z + H*vZ };

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  float[][] getCubitPositions(int numLayers)

    {

    if( numLayers<5 ) return CORNERS;

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    int numCubitsPerCenter = 5;

    int numCubits = NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge + NUM_CENTERS*numCubitsPerCenter;

    int index=0;

    final float[][] CENTERS = new float[numCubits][];

    for(int corner=0; corner<NUM_CORNERS; corner++)

      {

      computeBasicCornerVectors(corner);

      for(int part=0; part<numCubitsPerCorner; part++, index++)

        {

        CENTERS[index] = computeCorner(numCubitsPerCorner,numLayers,corner,part);

        }

      }

    for(int edge=0; edge<NUM_EDGES; edge++)

      {

      for(int part=0; part<numCubitsPerEdge; part++, index++)

        {

        CENTERS[index] = computeEdge(numLayers, edge, part );

        }

      }

    for(int center=0; center<NUM_CENTERS; center++)

      {

      for(int part=0; part<numCubitsPerCenter; part++, index++)

        {

        CENTERS[index] = computeCenter(numLayers,center, part);

        }

      }

    return CENTERS;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private int getQuat(int cubit, int numCubitsPerCorner, int numCubitsPerEdge)

    {

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      int corner = cubit/numCubitsPerCorner;

      return QUAT_CORNER_INDICES[corner];

      }

    if( cubit < NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int edge = (cubit-NUM_CORNERS*numCubitsPerCorner)/numCubitsPerEdge;

      return QUAT_EDGE_INDICES[edge];

      }

    if( numCubitsPerCorner==0 )

      {

      return QUAT_CORNER_INDICES[cubit];

      }

    else

      {

      cubit -= (NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge);

      int numCubitsPerCenter = 5;

      int face = cubit/numCubitsPerCenter;

      int index= cubit%numCubitsPerCenter;

      int corner=mCenterMap[face][index];

      return QUAT_CORNER_INDICES[corner];

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createCubitMesh(int cubit, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    int[] sizes = ObjectList.KILO.getSizes();

    int variants = sizes.length;

    int highestSize = sizes[variants-1];

    int lowestSize = sizes[0];

    int indexCornerEdge = (numLayers-lowestSize)/2 - (lowestSize==3 ? 1:0);

    MeshBase mesh;

    if( mNumCornerEdgeVariants>0 )

      {

      if( mCornerMeshes==null ) mCornerMeshes = new MeshBase[mNumCornerEdgeVariants];

      if( mEdgeMeshes  ==null ) mEdgeMeshes   = new MeshBase[mNumCornerEdgeVariants][highestSize-3];

      }

    if( mCenterMeshes==null ) mCenterMeshes = new MeshBase[variants];

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      if( mCornerMeshes[indexCornerEdge]==null )

        {

        float width = (numLayers/3.0f)/(numLayers-1);

        mCornerMeshes[indexCornerEdge] = FactoryCubit.getInstance().createMinxCornerMesh(numLayers,width);

        }

      mesh = mCornerMeshes[indexCornerEdge].copy(true);

      }

    else if( cubit<NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int type = computeEdgeType(cubit,numCubitsPerCorner,numCubitsPerEdge);  // left-top, right-top, left-second, right-second, left-third...

      if( mEdgeMeshes[indexCornerEdge][type]==null )

        {

        float tmp   = (numLayers/3.0f)/(numLayers-1);

        float height= tmp*COS18;

        float width = tmp + (type/2)*tmp*SIN18;

        mEdgeMeshes[indexCornerEdge][type] = FactoryCubit.getInstance().createKilominxEdgeMesh(numLayers,width,height, (type%2)==0 );

        }

      mesh = mEdgeMeshes[indexCornerEdge][type].copy(true);

      }

    else

      {

      int indexCenter = (numLayers-3)/2;

      if( mCenterMeshes[indexCenter]==null )

        {

        float width = (1+0.5f*(numLayers-3)*SIN18)*(numLayers/3.0f)/(numLayers-1);

        mCenterMeshes[indexCenter] = FactoryCubit.getInstance().createKilominxCenterMesh(width);

        }

      mesh = mCenterMeshes[indexCenter].copy(true);

      }

    Static4D q = QUATS[getQuat(cubit,numCubitsPerCorner,numCubitsPerEdge)];

    MatrixEffectQuaternion quat = new MatrixEffectQuaternion( q, new Static3D(0,0,0) );

    mesh.apply(quat,0xffffffff,0);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getCornerColor(int cubit, int cubitface, int numLayers, int numCubitsPerCorner)

    {

    if( cubitface<0 || cubitface>2 ) return NUM_TEXTURES;

    int part  = cubit % numCubitsPerCorner;

    int corner= cubit / numCubitsPerCorner;

    if( part==0 )

      {

      return mCornerFaceMap[corner][cubitface];

      }

    else

      {

      int N = (numCubitsPerCorner-1)/3;

      int block = (part-1) % N;

      int index = (part-1) / N;

      if( block< (numLayers-3)/2 )

        {

        switch(index)

          {

          case 0: return cubitface==1 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          case 1: return cubitface==0 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          case 2: return cubitface==2 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          }

        }

      else

        {

        switch(index)

          {

          case 0: return cubitface==0 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          case 1: return cubitface==2 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          case 2: return cubitface==1 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          }

        }

      }

    return NUM_TEXTURES;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getEdgeColor(int edge, int cubitface, int numCubitsPerEdge)

    {

    if( cubitface<0 || cubitface>1 ) return NUM_TEXTURES;

    int part    = edge % numCubitsPerEdge;

    int variant = edge / numCubitsPerEdge;

    part /=2;

    return (part==0 || cubitface==((part+1)%2)) ? mEdgeMap[variant][cubitface+2] + ((part+3)/2)*NUM_FACES : NUM_TEXTURES;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getCenterColor(int center, int cubitface, int numLayers)

    {

     if( numLayers==3 )

      {

      return cubitface>=0 && cubitface<3 ? mCornerFaceMap[center][cubitface] : NUM_TEXTURES;

      }

    return cubitface==mCenterFaceMap[center] ? center/5 + NUM_FACES*(numLayers-1)/2 : NUM_TEXTURES;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getFaceColor(int cubit, int cubitface, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      return getCornerColor(cubit,cubitface,numLayers,numCubitsPerCorner);

      }

    else if( cubit<NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int edge = cubit - NUM_CORNERS*numCubitsPerCorner;

      return getEdgeColor(edge,cubitface,numCubitsPerEdge);

      }

    else

      {

      int center = cubit-NUM_CORNERS*numCubitsPerCorner-NUM_EDGES*numCubitsPerEdge;

      return getCenterColor( center, cubitface, numLayers);

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  void createFaceTexture(Canvas canvas, Paint paint, int face, int left, int top)

    {

    int COLORS = FACE_COLORS.length;

    int variant = face/COLORS;

    int numLayers = getNumLayers();

    if( variant == (numLayers-1)/2 || numLayers==3 )

      {

      float S = 0.07f;

      float R = 0.09f;

      float A = 0.86f;

      float X1= (SQ5+1)/8;

      float Y1= (float)(Math.sqrt(2+0.4f*SQ5)/4);

      float Y2= Y1 - (float)(Math.sqrt(10-2*SQ5)/8);

      float[] vertices = { -X1, Y2, 0, -A*Y1, X1, Y2, 0, Y1 };

      FactorySticker factory = FactorySticker.getInstance();

      factory.drawRoundedPolygon(canvas, paint, left, top, vertices, S, FACE_COLORS[face%NUM_FACES], R);

      float MID = TEXTURE_HEIGHT*0.5f;

      float WID = TEXTURE_HEIGHT*0.1f;

      float HEI = TEXTURE_HEIGHT*(0.47f+Y1);

      canvas.drawLine(left+MID-WID,top+HEI,left+MID+WID,top+HEI,paint);

      }

    else if( variant==0 )

      {

      float Y = COS54/(2*SIN54);

      float R = 0.09f;

      float S = 0.09f;

      float[] vertices = { -0.5f, 0.0f, 0.0f, -Y, 0.5f, 0.0f, 0.0f, Y };

      FactorySticker factory = FactorySticker.getInstance();

      factory.drawRoundedPolygon(canvas, paint, left, top, vertices, S, FACE_COLORS[face%COLORS], R);

      }

    else

      {

      float R = 0.07f;

      float S = 0.07f;

      float tmp   = (numLayers/3.0f)/(numLayers-1);

      float height= tmp*COS18;

      float width = tmp + (variant-1)*tmp*SIN18;

      float D = height/COS18;

      float W = D*SIN18;

      float X1 = height/2;

      float Y1 = width/2;

      float[] vertices = { -X1,-Y1, X1, -Y1, X1, Y1+W,-X1, Y1 };

      FactorySticker factory = FactorySticker.getInstance();

      factory.drawRoundedPolygon(canvas, paint, left, top, vertices, S, FACE_COLORS[face%COLORS], R);

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// PUBLIC API

  public boolean isSolved()

    {

    int index = CUBITS[0].mQuatIndex;

    for(int i=1; i<NUM_CUBITS; i++)

      {

      if( thereIsVisibleDifference(CUBITS[i], index) ) return false;

      }

    return true;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public int getObjectName(int numLayers)

    {

    if( numLayers==3 ) return R.string.minx2;

    if( numLayers==5 ) return R.string.minx4;

    return 0;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public int getInventor(int numLayers)

    {

    if( numLayers==3 ) return R.string.minx2_inventor;

    if( numLayers==5 ) return R.string.minx4_inventor;

    return 0;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public int getComplexity(int numLayers)

    {

    return 3;

    }

}